Question 101
Let $A$ and $B$ be points on the circle $k$ with centre $O$ such that $A B \gt A O$. Let $C$ be the intersection point, different from $A$, of the angle bisector of $\angle O A B$ with $k$. Let $D$ be the intersection point, different from $B$, of the line $A B$ with the circumcircle of triangle $O B C$. Show that $A D = A O$.